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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 03 Dec 2008 14:39:45 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/03/t1228340527oo4vrpvs39905sy.htm/, Retrieved Fri, 17 May 2024 16:43:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28895, Retrieved Fri, 17 May 2024 16:43:48 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

193

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Exercise 1.13] [Exercise 1.13 (Wo...] [2008-10-01 13:28:34] [b98453cac15ba1066b407e146608df68]
- RMPD  [Univariate Data Series] [Tijdreeks 2: Gaso...] [2008-10-20 15:56:05] [a57f5cc542637534b8bb5bcb4d37eab1]
- RMP       [(Partial) Autocorrelation Function] [Identification/es...] [2008-12-03 21:39:45] [0f30549460cf4ec26d9cf94b1fcf7789] [Current]

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Dataseries X:

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Histogram

Boxplots

0.33
0.33
0.32
0.33
0.34
0.36
0.34
0.33
0.35
0.31
0.28
0.26
0.26
0.26
0.29
0.30
0.30
0.28
0.29
0.29
0.32
0.33
0.29
0.31
0.33
0.36
0.39
0.30
0.27
0.28
0.29
0.30
0.30
0.30
0.31
0.30
0.31
0.29
0.32
0.33
0.35
0.35
0.36
0.40
0.40
0.47
0.43
0.38
0.38
0.40
0.45
0.47
0.45
0.50
0.54
0.55
0.59
0.51
0.50
0.50

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28895&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28895&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28895&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.028721	0.2206	0.413079
2	-0.12014	-0.9228	0.179931
3	-0.159271	-1.2234	0.113024
4	-0.197465	-1.5168	0.067334
5	0.261008	2.0048	0.024788
6	0.034607	0.2658	0.395652
7	-0.192662	-1.4799	0.072114
8	-0.092443	-0.7101	0.240228
9	-0.026185	-0.2011	0.420643
10	0.196091	1.5062	0.068676
11	0.193872	1.4892	0.070886
12	-0.09927	-0.7625	0.224397
13	-0.040929	-0.3144	0.37717
14	-0.117493	-0.9025	0.185235
15	0.012033	0.0924	0.463336
16	-0.035258	-0.2708	0.393735
17	-0.026053	-0.2001	0.421039

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.028721 & 0.2206 & 0.413079 \tabularnewline
2 & -0.12014 & -0.9228 & 0.179931 \tabularnewline
3 & -0.159271 & -1.2234 & 0.113024 \tabularnewline
4 & -0.197465 & -1.5168 & 0.067334 \tabularnewline
5 & 0.261008 & 2.0048 & 0.024788 \tabularnewline
6 & 0.034607 & 0.2658 & 0.395652 \tabularnewline
7 & -0.192662 & -1.4799 & 0.072114 \tabularnewline
8 & -0.092443 & -0.7101 & 0.240228 \tabularnewline
9 & -0.026185 & -0.2011 & 0.420643 \tabularnewline
10 & 0.196091 & 1.5062 & 0.068676 \tabularnewline
11 & 0.193872 & 1.4892 & 0.070886 \tabularnewline
12 & -0.09927 & -0.7625 & 0.224397 \tabularnewline
13 & -0.040929 & -0.3144 & 0.37717 \tabularnewline
14 & -0.117493 & -0.9025 & 0.185235 \tabularnewline
15 & 0.012033 & 0.0924 & 0.463336 \tabularnewline
16 & -0.035258 & -0.2708 & 0.393735 \tabularnewline
17 & -0.026053 & -0.2001 & 0.421039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28895&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.028721[/C][C]0.2206[/C][C]0.413079[/C][/ROW]
[ROW][C]2[/C][C]-0.12014[/C][C]-0.9228[/C][C]0.179931[/C][/ROW]
[ROW][C]3[/C][C]-0.159271[/C][C]-1.2234[/C][C]0.113024[/C][/ROW]
[ROW][C]4[/C][C]-0.197465[/C][C]-1.5168[/C][C]0.067334[/C][/ROW]
[ROW][C]5[/C][C]0.261008[/C][C]2.0048[/C][C]0.024788[/C][/ROW]
[ROW][C]6[/C][C]0.034607[/C][C]0.2658[/C][C]0.395652[/C][/ROW]
[ROW][C]7[/C][C]-0.192662[/C][C]-1.4799[/C][C]0.072114[/C][/ROW]
[ROW][C]8[/C][C]-0.092443[/C][C]-0.7101[/C][C]0.240228[/C][/ROW]
[ROW][C]9[/C][C]-0.026185[/C][C]-0.2011[/C][C]0.420643[/C][/ROW]
[ROW][C]10[/C][C]0.196091[/C][C]1.5062[/C][C]0.068676[/C][/ROW]
[ROW][C]11[/C][C]0.193872[/C][C]1.4892[/C][C]0.070886[/C][/ROW]
[ROW][C]12[/C][C]-0.09927[/C][C]-0.7625[/C][C]0.224397[/C][/ROW]
[ROW][C]13[/C][C]-0.040929[/C][C]-0.3144[/C][C]0.37717[/C][/ROW]
[ROW][C]14[/C][C]-0.117493[/C][C]-0.9025[/C][C]0.185235[/C][/ROW]
[ROW][C]15[/C][C]0.012033[/C][C]0.0924[/C][C]0.463336[/C][/ROW]
[ROW][C]16[/C][C]-0.035258[/C][C]-0.2708[/C][C]0.393735[/C][/ROW]
[ROW][C]17[/C][C]-0.026053[/C][C]-0.2001[/C][C]0.421039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28895&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28895&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.028721	0.2206	0.413079
2	-0.12014	-0.9228	0.179931
3	-0.159271	-1.2234	0.113024
4	-0.197465	-1.5168	0.067334
5	0.261008	2.0048	0.024788
6	0.034607	0.2658	0.395652
7	-0.192662	-1.4799	0.072114
8	-0.092443	-0.7101	0.240228
9	-0.026185	-0.2011	0.420643
10	0.196091	1.5062	0.068676
11	0.193872	1.4892	0.070886
12	-0.09927	-0.7625	0.224397
13	-0.040929	-0.3144	0.37717
14	-0.117493	-0.9025	0.185235
15	0.012033	0.0924	0.463336
16	-0.035258	-0.2708	0.393735
17	-0.026053	-0.2001	0.421039

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.028721	0.2206	0.413079
2	-0.121065	-0.9299	0.178102
3	-0.154313	-1.1853	0.120325
4	-0.213121	-1.637	0.053475
5	0.24272	1.8644	0.033624
6	-0.052209	-0.401	0.344926
7	-0.222725	-1.7108	0.046188
8	-0.062026	-0.4764	0.317763
9	0.055046	0.4228	0.336983
10	0.076617	0.5885	0.279221
11	0.094886	0.7288	0.234493
12	-0.028893	-0.2219	0.412566
13	0.06896	0.5297	0.299156
14	-0.083718	-0.6431	0.261341
15	-0.028438	-0.2184	0.413921
16	-0.165947	-1.2747	0.103713
17	0.050725	0.3896	0.349107

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.028721 & 0.2206 & 0.413079 \tabularnewline
2 & -0.121065 & -0.9299 & 0.178102 \tabularnewline
3 & -0.154313 & -1.1853 & 0.120325 \tabularnewline
4 & -0.213121 & -1.637 & 0.053475 \tabularnewline
5 & 0.24272 & 1.8644 & 0.033624 \tabularnewline
6 & -0.052209 & -0.401 & 0.344926 \tabularnewline
7 & -0.222725 & -1.7108 & 0.046188 \tabularnewline
8 & -0.062026 & -0.4764 & 0.317763 \tabularnewline
9 & 0.055046 & 0.4228 & 0.336983 \tabularnewline
10 & 0.076617 & 0.5885 & 0.279221 \tabularnewline
11 & 0.094886 & 0.7288 & 0.234493 \tabularnewline
12 & -0.028893 & -0.2219 & 0.412566 \tabularnewline
13 & 0.06896 & 0.5297 & 0.299156 \tabularnewline
14 & -0.083718 & -0.6431 & 0.261341 \tabularnewline
15 & -0.028438 & -0.2184 & 0.413921 \tabularnewline
16 & -0.165947 & -1.2747 & 0.103713 \tabularnewline
17 & 0.050725 & 0.3896 & 0.349107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28895&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.028721[/C][C]0.2206[/C][C]0.413079[/C][/ROW]
[ROW][C]2[/C][C]-0.121065[/C][C]-0.9299[/C][C]0.178102[/C][/ROW]
[ROW][C]3[/C][C]-0.154313[/C][C]-1.1853[/C][C]0.120325[/C][/ROW]
[ROW][C]4[/C][C]-0.213121[/C][C]-1.637[/C][C]0.053475[/C][/ROW]
[ROW][C]5[/C][C]0.24272[/C][C]1.8644[/C][C]0.033624[/C][/ROW]
[ROW][C]6[/C][C]-0.052209[/C][C]-0.401[/C][C]0.344926[/C][/ROW]
[ROW][C]7[/C][C]-0.222725[/C][C]-1.7108[/C][C]0.046188[/C][/ROW]
[ROW][C]8[/C][C]-0.062026[/C][C]-0.4764[/C][C]0.317763[/C][/ROW]
[ROW][C]9[/C][C]0.055046[/C][C]0.4228[/C][C]0.336983[/C][/ROW]
[ROW][C]10[/C][C]0.076617[/C][C]0.5885[/C][C]0.279221[/C][/ROW]
[ROW][C]11[/C][C]0.094886[/C][C]0.7288[/C][C]0.234493[/C][/ROW]
[ROW][C]12[/C][C]-0.028893[/C][C]-0.2219[/C][C]0.412566[/C][/ROW]
[ROW][C]13[/C][C]0.06896[/C][C]0.5297[/C][C]0.299156[/C][/ROW]
[ROW][C]14[/C][C]-0.083718[/C][C]-0.6431[/C][C]0.261341[/C][/ROW]
[ROW][C]15[/C][C]-0.028438[/C][C]-0.2184[/C][C]0.413921[/C][/ROW]
[ROW][C]16[/C][C]-0.165947[/C][C]-1.2747[/C][C]0.103713[/C][/ROW]
[ROW][C]17[/C][C]0.050725[/C][C]0.3896[/C][C]0.349107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28895&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28895&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.028721	0.2206	0.413079
2	-0.121065	-0.9299	0.178102
3	-0.154313	-1.1853	0.120325
4	-0.213121	-1.637	0.053475
5	0.24272	1.8644	0.033624
6	-0.052209	-0.401	0.344926
7	-0.222725	-1.7108	0.046188
8	-0.062026	-0.4764	0.317763
9	0.055046	0.4228	0.336983
10	0.076617	0.5885	0.279221
11	0.094886	0.7288	0.234493
12	-0.028893	-0.2219	0.412566
13	0.06896	0.5297	0.299156
14	-0.083718	-0.6431	0.261341
15	-0.028438	-0.2184	0.413921
16	-0.165947	-1.2747	0.103713
17	0.050725	0.3896	0.349107

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code